I will try and answer what I - at the point of writing - understand is your questions:
Cryptography is platform independent, so it does not matter which platform is sending of receiving an encrypted message as long as the sender and receiver do adhere to the same protocol.
As to the key exchange: Let's say, you have devices A and B, both belonging to the same identity, I. Now, I is supposed to have access to messages through A and B. That either means each message is to be encrypted with key(A) and key(B) - or that key(A) = key(B).
In the first case, you cannot trust the server to not transparently add a third device under their control to the list of keys for I, i.e. key(C). This might raise some eyebrows with the sender, but as they are in control of the UI and for that - nevermind.
In the second case, you can share the keys by establishing a secure communications channel to transmit the key - for example by displaying a QR-Code on A and scanning it with B in a secure environment.
In both cases, as the UI and logic might me closed source or you might not be running the binary you have sources for (could be patched before delivery), you cannot be sure that either A nor B transmit all keys known to them to the server while you're texting away.
It boils down to: key exchange is a solvable problem for this scenario - trusting software isn't. You either do or don't and use your own software under your control, adhering to the same protocol.
As to you asking for the implementation and design details for a specific product: I don't know; it might not be disclosed. And if it were, if you're distrusting the supplier, why trust what They say?